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In a recent paper [A. Alberucci, C. Jisha, N. Smyth, and G. Assanto, Phys. Rev. A 91, 013841 (2015)], Alberucci et al. have studied the propagation of bright spatial solitary waves in highly nonlocal media. We find that the main results in that and related papers, concerning soliton shape and dynamics, based on the accessible soliton (AS) approximation, are incorrect; the correct results have already been published by others. These and other inconsistencies in the paper follow from the problems in applying the AS approximation in earlier papers by the group that propagated to the later papers. The accessible soliton theory cannot describe accurately the features and dynamics of solitons in highly nonlocal media., 2 pages

We investigate, both theoretically and numerically, a graphene-coated nano-cylinder illuminated by a plane electromagnetic wave in THz range of frequencies. We have derived an analytical formula that enables fast evaluation of the spectral window with a substantial reduction in scattering efficiency for sufficiently thin cylinder. This effect leads to tunable resonant invisibility that can be achieved via modification of graphene chemical potential monitored by the gate voltage. A multi-frequency cloaking mechanism based on dimer coated nanowires is also discussed.

The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimate of nonlinear Schrodinger (NLS) equations in R2 with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimate can be used to obtain the 2nd order term (which is of order $ln\Gamma$) of the lower bound of the ground state energy as the coefficient $\Gamma$ of the nonlinear term tends to infinity.

The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimate of nonlinear Schrodinger (NLS) equations in R2 with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimate can be used to obtain the 2nd order term (which is of order $ln��$) of the lower bound of the ground state energy as the coefficient $��$ of the nonlinear term tends to infinity.

We investigate surface waves at the boundary between a semi-infinite layered metal-dielectric nanostructure cut normally to the layers and a semi-infinite dielectric. Spatial dispersion properties of such a nanostructure can be dramatically affected by coupling of surface plasmons polaritons at different metal-dielectric interfaces. As a consequence, the effective medium approach is not applicable in general. It is demonstrated that Dyakonov-like surface waves with hybrid polarization can propagate in an angular range substantially enlarged compared to conventional birefringent materials. Our numerical simulations for an Ag-GaAs stack in contact with glass show a low to moderate influence of losses., Comment: 3 pages

We question physical existence of shape invariant solitons in three dimensional nematic liquid crystals. Using modified Petviashvili's method for finding eigenvalues and eigenfunctions, we determine shape invariant solitons in a realistic physical model that includes the highly nonlocal nature of the liquid crystal system. We check the stability of such solutions by propagating them for long distances. We establish that any noise added to the medium or to the fundamental solitons induces them to breathe, rendering them practically unobservable., Comment: 4 pages, 4 figures

Various algebraic structures of degenerate four-wave mixing equations of optical phase conjugation are analyzed. Two approaches (the spinorial and the Lax-pair based), complementary to each other, are utilized for a systematic derivation of conserved quantities. Symmetry groups of both the equations and the conserved quantities are determined, and the corresponding generators are written down explicitly. Relation between these two symmetry groups is found. Conserved quantities enable the introduction of new methods for integration of the equations in the cases when the coupling $\Gamma$ is either purely real or purely imaginary. These methods allow for both geometries of the process, namely the transmission and the reflection, to be treated on an equal basis. One approach to introduction of Hamiltonian and Lagrangian structures for the 4WM systems is explored, and the obstacles in successful implementation of that programe are identified. In case of real coupling these obstacles are removable, and full Hamiltonian and Lagrangian formulations of the initial system are possible.